Undergraduate Classes

Intermediate Micro with Game Theory

Here are my lecture notes (including exercises) of Intermediate Microeconomics with some game theory, taught at Carngie Mellon University during my visit there.  The aim is again to provide a compact and self-contained set of materials that are accessible to students of diverse mathematical preparedness, and are rigorous enough to engage their mind. I select and sequence the game theory materials to convey a sense of continuance from the main component of this course, classic decision theory, to game theory.  First come zero-sum games that can be solved as if a consumer's optimization, owing to the minimax theorem. Then are games with dominant strategies where a player can to some extent make decisions regardless of the actions of the opponents. Finally comes an introduction of Nash equilibrium, where decisions are truly interactive across players.

 

Lectures Notes of Intermediate Microeconomics
Chapter Contents PDF
1: Output Supply first- & second-order conditions;  cost curves;  pure competition vs monopoly PDF
2: Input Deployment level surface; implicit function; supporting hyperplane; returns to scale PDF
3: The Lagrange Method mainly on equality constraints;  gradients;  some cases with inequality constraints PDF
4: Preference and Utility binary relation;  preference relation;  lexicographic ordering;  expected utility PDF
5: Consumer's Decision quasilinear utility functions;  corner vs interior solutions PDF
6: Revealed Preference substitution effect;  interpersonal welfare comparison;  axioms of revealed preference PDF
7: Zero Sum Games mixed strategy;  convex hull;  security strategy;  security level;  saddle point PDF
8: Dominant Strategies strict & weak dominance; backward induction; normal form & strategy; Stackelberg PDF
9: Nash Equilibrium pure & totally mixed strategy equilibrium; best response; fixed point; Cournot PDF

Intermediate Micro: Purely Decision Theory

Here are my lecture notes (including exercises) for the non-game-theoretic part of Intermediate Microeconomics.  They are aimed at compactifying the various topics into just several chapters under a single theme of introducing the formal analysis of decision making in the pure competition context.  I found such compactification conducive to striking a balance between the goal to engage the students in nontrivial economic reasoning---mathematics an integral part of the reasoning---and the constraints imposed by the large number of students and their vastly diverse levels of preparedness in critical reasoning.  With only a few chapters to read, students would be less distracted by the burden of memorizing jargons in various topics but rather focus more on the recurring theme, which deepens along the sequence of the chapters and culminates in the epilogue that introduces the modern envelope theorem.  The unconventional sequencing of the chapters, presenting first producer theory rather than consumer theory, is motivated by the fact that producer theory is simpler in substance, with explicit objective functions and without the income effect complication, and the concern that a consumer's decision tends to sound too close to students' daily experience for them to suspend the concrete for the abstract.

 

Lectures Notes of Intermediate Microeconomics 1
Chapter Contents PDF
1: Firm's Supply derivative; first- and second-order conditions; L'Hôpital's rule; proof by contradiction PDF
2: Input-Output Decision concavity;  supporting hyperplane;  proof PDF
3: Deployment of Inputs partial derivative;  implicit function;  proof PDF
4: The Lagrange Method vector;  gradient PDF
5: Preference and Utility binary relation;  countability;  continuity;  gamble;  expected utility PDF
6: Consumer's Decision corner solution PDF
7: Demand Function integration PDF
8: Slutsky Equation chain rule;  partial derivative PDF
9: Revealed Preference logic;  mathematical induction PDF
10. The Envelope Theorem partial derivative;  measure zero PDF